"We don't plan to trade Carson," Brown told the NFL Network at the league's spring owners meetings in Indianapolis. "He's important to us. He's a very fine player, and we do want him to come back. If he chooses not to, he'd retire. And we would go with Andy Dalton, the younger player we drafted, who's a good prospect.
"Ideally, we'd have both of them. That'd be the best way to go forward. If we don't have Carson, we'll go with Andy."
Brown also had said in January that the Bengals had no plans to trade Palmer. Monday's comments made it clear he hadn't softened his stance on the quarterback's future with the team.
The Bengals drafted Dalton, who led TCU to a Rose Bowl victory last season, with their second-round pick in April's draft.
Brown's comments echoed those of coach Marvin Lewis, who earlier this month said Palmer would be the starter this season, even though the quarterback has told the team he wants to be traded.
Palmer sold his house in Cincinnati this offseason, and according to WCPO-TV in Cincinnati, told a confidant earlier in the offseason that he "will never set foot in Paul Brown Stadium again.
Palmer hasn't talked to the media since making his trade request. He told SI.com at Drew Brees' celebrity golf tournament in San Diego last week that he remains on "media hiatus."
Palmer was the franchise's building block when it made him the first overall pick in 2003, Lewis' first season as coach. He led the Bengals to the playoffs in 2005 and 2009 -- their only winning records in the past 20 years -- and rebounded from severe knee and elbow injuries along the way.